LightTruncateSersic

class dysmalpy.models.LightTruncateSersic(tracer=None, **kwargs)

Bases: LightModel, _DysmalFittable1DModel

Light distribution following a Sersic profile. Can be truncted.

Parameters:

• r_eff (float) – Effective (half-light) radius in kpc

• L_tot (float) – Total luminsoity of untruncated Sersic profile. Arbitrary units.

• n (float) – Sersic index

• r_inner (float) – Inner truncation radius in kpc. Default: 0 kpc (untruncated)

• r_outer (float) – Outer truncation radius in kpc. Default: np.inf kpc (untruncated)

• tracer (string) – (Attribute): Name of the dynamical tracer

Notes

Model formula:

\[I(R) = I_e \exp \left\{ -b_n \left[ \left( \frac{R}{R_{\mathrm{eff}}} \right)^{1/n} -1 \right] \right\}\]

The constant \(b_n\) is defined such that \(R_{\mathrm{eff}}\) contains half the total light, and can be solved for numerically as:

\[\Gamma(2n) = 2\gamma (b_n,2n)\]

Examples

import numpy as np
from dysmalpy.models import LightTruncateSersic
import matplotlib.pyplot as plt

plt.figure()
plt.subplot(111, xscale='log', yscale='log')
ls1 = LightTruncateSersic(r_eff=5, n=1, r_inner=1, r_outer=20, L_tot=1.e11, tracer='halpha')
r=np.arange(0, 100, .01)

for n in range(1, 10):
     ls1.n = n
     plt.plot(r, ls1(r), color=str(float(n) / 15))

plt.axis([0.8, 27, 1e5, 1e10])
plt.xlabel('log Radius [kpc]')
plt.ylabel('log Intensity Surface Density [log Lsun/kpc^2]')
plt.text(1.1, 7.e8, 'n=1')
plt.text(1.1, 3.e9, 'n=10')
plt.show()

(Source code, png, hires.png, pdf)

Attributes Summary

L_tot
n
param_names	Names of the parameters that describe models of this type.
r_eff
r_inner
r_outer

Methods Summary

evaluate(r, L_tot, r_eff, n, r_inner, r_outer)	Sersic light surface density.
light_profile(r)	Conversion from mass to light as a function of radius

Attributes Documentation

L_tot = DysmalParameter('L_tot', value=1.0, bounds=(0, 50), prior=<dysmalpy.parameters.UniformPrior object>)

n = DysmalParameter('n', value=1.0, bounds=(0, 8), prior=<dysmalpy.parameters.UniformPrior object>)

param_names = ('L_tot', 'r_eff', 'n', 'r_inner', 'r_outer')

Names of the parameters that describe models of this type.

The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.

When defining a custom model class the value of this attribute is automatically set by the Parameter attributes defined in the class body.

r_eff = DysmalParameter('r_eff', value=1.0, bounds=(0, 50), prior=<dysmalpy.parameters.UniformPrior object>)

r_inner = DysmalParameter('r_inner', value=0.0, bounds=(0, 10), prior=<dysmalpy.parameters.UniformPrior object>)

r_outer = DysmalParameter('r_outer', value=inf, bounds=(0, inf), prior=<dysmalpy.parameters.UniformPrior object>)

Methods Documentation

static evaluate(r, L_tot, r_eff, n, r_inner, r_outer)

Sersic light surface density. Same as self.light_profile

light_profile(r)

Conversion from mass to light as a function of radius

Parameters:

r (float or array) – Radii at which to calculate the enclosed mass

Returns:

light – Relative line flux as a function of radius

Return type:

float or array